Deterministic tree pushdown automata and monadic tree rewriting systems
Journal of Computer and System Sciences
Grammars with controlled derivations
Handbook of formal languages, vol. 2
Term rewriting and all that
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Theoretical Computer Science
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Information and Computation
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LICS '95 Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science
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LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
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Journal of Computer and System Sciences - Special issue on PODS 2000
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Journal of the ACM (JACM)
Deleting string rewriting systems preserve regularity
Theoretical Computer Science - Developments in language theory
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Journal of Automated Reasoning
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Theoretical Computer Science
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FroCoS '07 Proceedings of the 6th international symposium on Frontiers of Combining Systems
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
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Information and Computation
Tree automata for rewrite strategies
Journal of Symbolic Computation
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Proceedings of the 12th international ACM SIGPLAN symposium on Principles and practice of declarative programming
Abstract regular tree model checking of complex dynamic data structures
SAS'06 Proceedings of the 13th international conference on Static Analysis
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Motivated by the problem of verification of imperative tree transformation programs, we study the combination, called controlled term rewriting systems (CntTRS), of term rewriting rules with constraints selecting the possible rewrite positions. These constraints are specified, for each rewrite rule, by a selection automaton which defines a set of positions in a term based on tree automata computations. We show that reachability is PSPACE-complete for so-called monotonic CntTRS, such that the size of every left-hand-side of every rewrite rule is larger or equal to the size of the corresponding right-hand-side, and also for the class of context-free non-collapsing CntTRS, which transform Context-Free (CF) tree language into CF tree languages. When allowing size-reducing rules, reachability becomes undecidable, even for flat CntTRS (both sides of rewrite rules are of depth at most one) when restricting to words (i.e. function symbols have arity at most one), and for ground CntTRS (rewrite rules have no variables). We also consider a restricted version of the control such that a position is selected if the sequence of symbols on the path from that position to the root of the tree belongs to a given regular language. This restriction enables decision results in the above cases.